When asked to defend musical theatre – and this happens annoyingly often – I always return to one show: West Side Story. For every criticism levelled at the genre, West Side Story has the answer. There is Leonard Bernstein's rich score, Stephen Sondheim's vibrant lyrics and Jerome Robbins's exuberant choreography. For me, it is a nigh-on perfect musical – and a matchless piece of theatre.

Strip everything else away – the thrilling dancing, imposing set and powerful plot, inspired by Romeo and Juliet – and West Side Story remains a brilliant musical composition. Bernstein was a classical musician first, a composer of musicals second. One of the songs in West Side Story – One Hand, One Heart – was originally intended for his operetta Candide. Such a complex score demands brilliant musicians, which means star casting is simply not an option. The two romantic leads, Tony and Maria (Tony is a member of a New York street gang and Maria comes from a community of Puerto Rican immigrants), are hugely challenging roles. Tony covers nearly two octaves; Maria soars up to an ear-splitting top C. Only the seriously musically talented need apply.

There isn't a duff song in the whole score. Something's Coming, Tony's first solo number, is shot through with fast and varied rhythms. Whenever I go on a date I think of this song, packed with jittery butterflies and giddy optimism. Maria is one of the most tender love songs ever written. I sing it often (as my frayed songbook will attest) and it always makes me glow. And then there is the devastating duet Somewhere. The yearning that stretches – painfully and beautifully – throughout this love song feels universal but also deeply personal.

West Side Story is also very funny, largely thanks to Sondheim's witty lyrics. In America, Sondheim contrasts the optimism of the Puerto Rican women, who are keen to assimilate to American life, with the jaded views of their men. With a few deft phrases, Sondheim highlights the gulf between the great expectations and grim reality faced by immigrants living in 1950s America: "Everything free in America / For a small fee in America!"

Gee, Officer Krupke is as funny as it is socially astute. There is a naivety to this number, with its larky choreography, which allows Bernstein and Sondheim to stick the knife in. As a bunch of "delinquent" men prance in bonnets, they jokily sing about their "junky" mums and alcoholic dads. The lads are sent ricocheting between judges, analysts, psychiatrists and doctors. It is a brilliant number, which always gets the audience chuckling, but Krupke is also a damning indictment of a society that refuses to take responsibility for its young and is then surprised and appalled when they end up in street gangs.

Then there is Robbins's instinctive choreography, which complements the music so brilliantly. Cool is made 10 times edgier by the persistent clicking and toe-tapping that underpins it. The Jet Song, with its surging lines of dancers, reflects the collective power and grace that the gang members find in each other. Robbins's choreography also accents the differences between the two gangs, contrasting the sharp high kicks of the Puerto Ricans with the cool shimmies of their American counterparts.

West Side Story is the musical I once sang with my grandma and the one I still sing with my sister and boyfriend. It is the musical that my father, a great musician, adores above all others; it always stimulates passionate chat between the two of us. It is the musical that binds me with my family.

Stephen Sondheim's serial-killing barber may be an unsavoury hero, but the musical skilfully mixes savagery, tragedy and comedy to create a work of art that leaves one in awe, writes Michael Billington